Continuous interior penalty finite element methods for the time-harmonic Maxwell equation with high wave number

In this paper, using the first-order Nedelec conforming edge element space of the second type, we develop and analyze a continuous interior penalty finite element method (CIP-FEM) for the time-harmonic Maxwell equation in the three-dimensional space. Compared with the standard finite element methods, the novelty of the proposed method is that we penalize the jumps of the tangential component of its vorticity field. It is proved that if the penalty parameter is a complex number with negative imaginary part, then the CIP-FEM is well-posed without any mesh constraint. The error estimates for the CIP-FEM are derived. Numerical experiments are presented to verify our theoretical results.

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